How do you integrate $int e^(2x)/(1+e^(2x))dx$ ?

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Answer 1 · 2016-11-21T06:00:20

The answer is $=1/2ln(1+e^(2x))+C$

Let's do it by substitution

Let $u=1+e^(2x)$

then, $du=2e^(2x)dx$

$int(e^(2x)dx)/(1+e^(2x))$

$=1/2int(du)/u=1/2lnabsu$

$=1/2ln(1+e^(2x))+C$

How do you integrate int e^(2x)/(1+e^(2x))dxint e^(2x)/(1+e^(2x))dx?